Finite Group Databasebeta

← #7655966

Subgroups — #7655966

Order 512.

5980 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42907C216yesmaximal, complemented
2#42895C216yesmaximal, complemented
3#42855C216yesmaximal, complemented
4#42838C216yesmaximal, complemented
5#39383C213yesmaximal, complemented
6#39375C213yesmaximal, complemented
7#39144C216yesmaximal, complemented
8#37493C216yesmaximal, complemented
9#36577C211yesmaximal, characteristic, complemented
10#36576C211yesmaximal, characteristic, complemented
11#36429C212yesmaximal, complemented
12#36049C212yesmaximal, complemented
13#36029C212yesmaximal, complemented
14#36005C212yesmaximal, complemented
15#35898C212yesmaximal, complemented
16#35005C213yesmaximal, complemented
17#34570C213yesmaximal, complemented
18#34294C212yesmaximal, complemented
19C2×#2341C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C2×#557C2211yescharacteristic, complemented
22C2×#550C2212yes—
23C2×#550C2212yes—
24C2×#550C2211yescharacteristic, complemented
25C2×#548C2212yes—
26C2×#538C2216yes—
27C2×#520C2212yescomplemented
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30#2857C2213yes—
31#2856C2213yes—
32#2847C2216yes—
33#2829C22112yescomplemented
34#2828C22112yescomplemented
35#2780C22112yescomplemented
36#2779C22112yescomplemented
37#2778C22112yescomplemented
38#2733C2216yescomplemented
39#2727C2216yescomplemented
40#2714C22112yescomplemented
41#2710C22112yescomplemented
42#2708C22112yescomplemented
43#2682C2216yescomplemented
44#2682C2216yescomplemented
45#2661C22112yescomplemented
46#2653C2216yescomplemented
47#2652C2216yescomplemented
48#2649C2216yescomplemented
49#2648C2216yescomplemented
50#2648C22112yescomplemented
51#2646C2211yescharacteristic
52#2644C2216yescomplemented
53#2643C2216yes—
54#2641C2216yescomplemented
55#2639C2213yes—
56#2626C2213yes—
57#2624C2216yescomplemented
58#2622C2216yes—
59#2619C2216yescomplemented
60#2617C2213yes—
61#2617C2216yes—
62#2582C2213yescomplemented
63#2568C2213yescomplemented
64#2562C2216yescomplemented
65#2559C22112yescomplemented
66#2557C22112yescomplemented
67#2548C2216yescomplemented
68#2548C2213yescomplemented
69#2541C2216yescomplemented
70#2538C2213yescomplemented
71#2535C2216yescomplemented
72#2513C2216yescomplemented
73#2512C2216yescomplemented
74#2512C2216yescomplemented
75#2501C2216yescomplemented
76#2497C2216yescomplemented
77#2496C2216yescomplemented
78#2494C2216yescomplemented
79#2491C2216yescomplemented
80#2491C2216yescomplemented
81#2490C2216yescomplemented
82#2490C2216yescomplemented
83#2487C2216yescomplemented
84#2453C2216yescomplemented
85#2445C2216yescomplemented
86#2445C2216yescomplemented
87#2442C2216yes—
88#2433C2216yes—
89#2431C2216yes—
90#2431C2216yes—
91#2428C2216yescomplemented
92#2428C2216yescomplemented
93#2426C2216yescomplemented
94#2424C22112yes—
95#2422C2216yescomplemented
96#2422C2216yescomplemented
97#2418C22112yes—
98#2416C2216yes—
99#2416C2216yescomplemented
100#2416C2216yescomplemented
101#2408C2216yes—
102#2407C2216yes—
103#2407C2216yes—
104#2401C2216yescomplemented
105#2398C2216yescomplemented
106#2395C2216yescomplemented
107#2392C2216yescomplemented
108#2367C2216yescomplemented
109#2361C2216yes—
110#2360C2216yescomplemented
111#2351C2212yescomplemented
112Q8×C4⋊C4C2211yescharacteristic, complemented
113Q8×C4⋊C4C2212yescomplemented
114Q8×C4⋊C4C2211yescharacteristic, complemented
115D4×C4⋊C4C2216yes—
116#2341C2212yes—
117#2341C2216yes—
118#2341C2216yes—
119#2341C2212yes—
120#2341C2212yes—
121#2341C2212yes—
122#2341C2212yescomplemented
123#2341C2212yescomplemented
124Q8×C22⋊C4C2212yes—
125#2326C2216yescomplemented
126#2325C2216yes—
127#2323C2216yescomplemented
128C4×C22⋊Q8C2213yes—
129C4×#121C2213yes—
130C4×#121C2216yes—
131C4×#120C2216yes—
132C2×#390C2213yes—
133C2×#390C2213yes—
134#2290C2216yes—
135C2×#380C2213yes—
136#2276C2212yescomplemented
137C2×C4×C22⋊C4C2213yes—
138C22×#41—28no—
139C22×#41—44no—
140C22×#41—44no—
141C22×#41C2312yes—
142C22×#41C2312yes—
143C22×#41C2316yes—
144C23×Q8C2311yescharacteristic
145C23×D4C2313yes—
146C24×C4C2313yes—
147#557—44no—
148#550—48no—
149#550—48no—
150#550—44no—
151#548—216no—
152#538—424no—
153C2×C4⋊Q8C2313yes—
154C2×#127C2313yes—
155C2×#127C2316yes—
156C2×#127C2316yes—
157C2×#126C23112yes—
158C2×#125C2316yes—
159C2×#124C2316yes—
160C2×#124C23112yes—
161C2×#123C23112yes—
162C2×#123C23112yes—
163C2×C22⋊Q8C2316yes—
164C2×C22⋊Q8C2313yes—
165C2×#121C2316yes—
166C2×#121C2313yes—
167C2×#121C2316yes—
168C2×#121C2316yes—
169C2×#121C2316yes—
170C2×#121C2316yes—
171C2×#121C2316yes—
172C2×#121C2316yes—
173C2×#121C23112yes—
174C2×#121C23112yes—
175C2×#120C23112yes—
176C2×#120C2316yes—
177#520—48no—
178C2×C4×Q8—44no—
179C2×C4×Q8—44no—
180C2×C4×Q8C2312yes—
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2311yescharacteristic
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2312yes—
185C2×C4×Q8C2311yescharacteristic
186C2×C4×Q8C2313yes—
187C2×C4×Q8C2316yes—
188C2×C4×Q8C2313yes—
189C2×C4×Q8C2313yes—
190C2×C4×D4C2316yes—
191C2×C4×D4C2316yes—
192C2×C4×D4C23112yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C2316yes—
195C2×C4×D4C2313yes—
196C2×C4×D4C2316yes—
197C2×#117C2316yes—
198C22×C4⋊C4C2313yes—
199C22×C4⋊C4C2316yes—
200C22×C4⋊C4C2313yes—
201C22×C22⋊C4C2313yes—
202C22×C22⋊C4C2313yes—
203C22×C22⋊C4C2316yes—
204C22×C42C2313yes—
205C22×C42C2313yes—
206#401C2316yes—
207#400C2316yes—
208#400C23112yes—
209#400C2316yes—
210#400C2316yes—
211#400C2316yes—
212#400C2312yes—
213#400C2312yes—
214#399C23112yes—
215#399C2316yes—
216#398C23112yes—
217#398C2312yes—
218#398C2312yes—
219#397C2316yes—
220#397C23112yes—
221#397C2316yes—
222#397C23112yes—
223#397C2316yes—
224#397C2316yes—
225#397C2316yes—
226#397C2316yes—
227#397C2316yes—
228#397C2316yes—
229#397C2316yes—
230#396C23112yes—
231#396C23112yes—
232#396C2316yes—
233#396C2316yes—
234#396C2316yes—
235#394C23112yes—
236#394C2316yes—
237#394C23112yes—
238#394C23112yes—
239#394C23112yes—
240#394C23112yes—
241#394C2316yes—
242#394C23112yes—
243#394C23112yes—
244#394C23112yes—
245#394C2316yes—
246#394C2316yes—
247#394C2316yes—
248#394C2316yes—
249#394C2316yes—
250#393C2316yes—
251#393C2316yes—
252#392C23112yes—
253#392C23112yes—
254#392C23112yes—
255#392C23112yes—
256#392C23112yes—
257#392C2316yes—
258#391C2313yes—
259#391C2316yes—
260#391C2316yes—
261#391C2316yes—
262#390C23112yes—
263#390C2316yes—
264#390C2316yes—
265#390C2316yes—
266#390C2316yes—
267#390C2316yes—
268#390C2316yes—
269#390C2316yes—
270#390C2316yes—
271#390C2316yes—
272#390C2316yes—
273#390C2316yes—
274#390C2316yes—
275#390C2316yes—
276#390C2316yes—
277#390C2316yes—
278#390C2316yes—
279#390C2313yes—
280#390C23112yes—
281#389C23112yes—
282#389C2316yes—
283#389C2313yes—
284#389C2316yes—
285#389C2316yes—
286#389C2316yes—
287#389C2316yes—
288#389C2316yes—
289#389C2316yes—
290#389C2313yes—
291#388C23112yes—
292#388C23112yes—
293#388C2316yes—
294#388C23112yes—
295#388C23112yes—
296#388C2316yes—
297#388C23112yes—
298#388C2316yes—
299#388C23112yes—
300#387C2316yes—
301#387C2316yes—
302#387C23112yes—
303#387C2316yes—
304#386C2316yes—
305#386C23112yes—
306#386C23112yes—
307#386C23112yes—
308#386C2316yes—
309#386C2316yes—
310#386C2316yes—
311#386C2316yes—
312#386C2316yes—
313#386C23112yes—
314#386C23112yes—
315#385C23112yes—
316#385C23112yes—
317#385C23112yes—
318#385C2316yes—
319#385C2312yes—
320#385C2316yes—
321#385C2312yes—
322#385C2316yes—
323#385C2316yes—
324#384C2316yes—
325#384C2313yes—
326#384C2313yes—
327#382C2316yes—
328#380C2316yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335#380C2316yes—
336#380C23112yes—
337#380C2311yescharacteristic
338#380C2311yescharacteristic
339#379C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2313yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2313yes—
346C4×C4⋊C4C2316yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C23112yes—
357#376C2316yes—
358C2×#95C2313yes—
359C2×#95C2311yescharacteristic
360C25C2413yes—
361C2×#41—28no—
362C2×#41—224no—
363C2×#41—28no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—28no—
368C2×#41—412no—
369C2×#41—412no—
370C2×#41—464no—
371C22×Q8—24no—
372C22×Q8—24no—
373C22×Q8#4118yes—
374C22×Q8C2413yes—
375C22×Q8C2413yes—
376C22×Q8C2411yescharacteristic
377C22×D4—212no—
378C22×D4—46no—
379C22×D4—46no—
380C22×D4C2416yes—
381C22×D4C2416yes—
382C22×D4C2416yes—
383C22×D4C2413yes—
384C22×D4C2416yes—
385C22×D4C2416yes—
386C22×D4C2416yes—
387C22×D4C24112yes—
388C22×D4C24112yes—
389C22×D4C2416yes—
390C23×C4—212no—
391C23×C4—46no—
392C23×C4—46no—
393C23×C4C2416yes—
394C23×C4C2416yes—
395C23×C4C2413yes—
396C23×C4C2413yes—
397C23×C4C2413yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2416yes—
401C23×C4C24112yes—
402C23×C4C2411yescharacteristic
403C4⋊Q8—46no—
404#127—46no—
405#127—412no—
406#127—412no—
407#126—424no—
408#125—412no—
409#124—224no—
410#124—424no—
411#123—424no—
412#123—812no—
413C22⋊Q8—224no—
414C22⋊Q8—212no—
415#121—224no—
416#121—212no—
417#121—424no—
418#121—412no—
419#121—412no—
420#121—412no—
421#121—412no—
422#121—412no—
423#121—412no—
424#121—812no—
425#120—412no—
426#120—424no—
427C4×Q8—28no—
428C4×Q8—28no—
429C4×Q8—24no—
430C4×Q8—24no—
431C4×Q8—28no—
432C4×Q8—28no—
433C4×Q8—46no—
434C4×Q8—412no—
435C4×Q8—46no—
436C4×Q8—46no—
437C4×D4—224no—
438C4×D4—412no—
439C4×D4—412no—
440C4×D4—46no—
441C4×D4—412no—
442C4×D4—412no—
443C4×D4—424no—
444#117—412no—
445C2×C4⋊C4—46no—
446C2×C4⋊C4—46no—
447C2×C4⋊C4—412no—
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2413yes—
451C2×C4⋊C4C2413yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2413yes—
457C2×C4⋊C4C2413yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2416yes—
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C24112yes—
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2416yes—
468C2×C4⋊C4C2416yes—
469C2×C4⋊C4C2416yes—
470C2×C4⋊C4C2416yes—
471C2×C4⋊C4C2416yes—
472C2×C4⋊C4C2416yes—
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C4⋊C4C2412yes—
476C2×C22⋊C4—212no—
477C2×C22⋊C4—46no—
478C2×C22⋊C4—86no—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2412yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2412yes—
485C2×C22⋊C4C24112yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C24112yes—
488C2×C22⋊C4C24112yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C2416yes—
496C2×C22⋊C4C2416yes—
497C2×C22⋊C4C2416yes—
498C2×C22⋊C4C24112yes—
499C2×C22⋊C4C24112yes—
500C2×C22⋊C4C24112yes—
501C2×C22⋊C4C2416yes—
502C2×C22⋊C4C2416yes—
503C2×C22⋊C4C2416yes—
504C2×C22⋊C4C24112yes—
505C2×C22⋊C4C2416yes—
506C2×C22⋊C4C2416yes—
507C2×C22⋊C4C2416yes—
508C2×C22⋊C4C2416yes—
509C2×C42—46no—
510C2×C42—46no—
511C2×C42C2416yes—
512C2×C42C2416yes—
513C2×C42C2416yes—
514C2×C42C2413yes—
515C2×C42C2416yes—
516C2×C42C2413yes—
517C2×C42C24112yes—
518C2×C42C2416yes—
519C2×C42C2413yes—
520C2×C42C2413yes—
521#95C2412yes—
522#95C2412yes—
523#95C2416yes—
524#95C2416yes—
525#95C2412yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C2412yes—
530#95C2412yes—
531#95C2412yes—
532#95C2412yes—
533#95C2416yes—
534#95C2416yes—
535#95C2416yes—
536#95C2416yes—
537#95C2416yes—
538#95C24112yes—
539#95C2416yes—
540#95C2416yes—
541#95C2412yes—
542#95C2416yes—
543#95C2416yes—
544#95C2416yes—
545#95C2416yes—
546#95C24112yes—
547C24—26no—
548C24—26no—
549C24—26no—
550C24—43no—
551C24—43no—
552C24—43no—
553C24—43no—
554C24C2516yes—
555C24C2516yes—
556C24C2511yescharacteristic
557#41—496no—
558#41—432no—
559#41—432no—
560C2×Q8—232no—
561C2×Q8—26no—
562C2×Q8—26no—
563C2×Q8—26no—
564C2×Q8—43no—
565C2×Q8—43no—
566C2×Q8C2×#41112yes—
567C2×Q8C2×#4114yes—
568C2×Q8H(5,𝔽2)14yes—
569C2×Q8H(5,𝔽2)14yes—
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—212no—
573C2×D4—212no—
574C2×D4—212no—
575C2×D4—212no—
576C2×D4—212no—
577C2×D4—212no—
578C2×D4—212no—
579C2×D4—212no—
580C2×D4—26no—
581C2×D4—46no—
582C2×D4—46no—
583C2×D4—448no—
584C2×D4—43no—
585C2×D4—46no—
586C2×D4—46no—
587C2×D4—46no—
588C2×D4—46no—
589C2×D4—46no—
590C2×D4—43no—
591C2×D4—46no—
592C2×D4—412no—
593C2×D4—412no—
594C2×D4—46no—
595C2×D4—412no—
596C2×D4—412no—
597C2×D4—46no—
598C2×D4—46no—
599C2×D4—412no—
600C2×D4—412no—
601C22×C4—26no—
602C22×C4—26no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—26no—
606C22×C4—26no—
607C22×C4—212no—
608C22×C4—212no—
609C22×C4—212no—
610C22×C4—212no—
611C22×C4—212no—
612C22×C4—212no—
613C22×C4—212no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—46no—
619C22×C4—46no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—43no—
623C22×C4—43no—
624C22×C4—43no—
625C22×C4—43no—
626C22×C4—412no—
627C22×C4—412no—
628C22×C4—412no—
629C22×C4—448no—
630C22×C4C2×#41112yes—
631C22×C4H(5,𝔽2)14yes—
632C22×C4C2512yes—
633C22×C4C2512yes—
634C22×C4C2512yes—
635C22×C4C2512yes—
636C22×C4C2516yes—
637C22×C4C2512yes—
638C22×C4C2513yes—
639C22×C4C2516yes—
640C22×C4C2516yes—
641C22×C4C2512yes—
642C22×C4C2516yes—
643C22×C4C2513yes—
644C22×C4C2513yes—
645C22×C4C2511yescharacteristic
646C22×C4C2511yescharacteristic
647C22×C4C2513yes—
648C4⋊C4—212no—
649C4⋊C4—212no—
650C4⋊C4—212no—
651C4⋊C4—212no—
652C4⋊C4—26no—
653C4⋊C4—26no—
654C4⋊C4—212no—
655C4⋊C4—26no—
656C4⋊C4—212no—
657C4⋊C4—26no—
658C4⋊C4—46no—
659C4⋊C4—46no—
660C4⋊C4—46no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—41no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—412no—
669C4⋊C4—41no—
670C4⋊C4—46no—
671C4⋊C4—46no—
672C4⋊C4—46no—
673C4⋊C4—46no—
674C4⋊C4—46no—
675C4⋊C4—46no—
676C22⋊C4—24no—
677C22⋊C4—212no—
678C22⋊C4—24no—
679C22⋊C4—212no—
680C22⋊C4—224no—
681C22⋊C4—212no—
682C22⋊C4—212no—
683C22⋊C4—212no—
684C22⋊C4—46no—
685C22⋊C4—46no—
686C22⋊C4—412no—
687C22⋊C4—412no—
688C22⋊C4—46no—
689C22⋊C4—46no—
690C22⋊C4—46no—
691C22⋊C4—46no—
692C22⋊C4—46no—
693C22⋊C4—46no—
694C22⋊C4—46no—
695C22⋊C4—46no—
696C22⋊C4—46no—
697C22⋊C4—412no—
698C22⋊C4—46no—
699C22⋊C4—46no—
700C22⋊C4—412no—
701C22⋊C4—412no—
702C22⋊C4—412no—
703C22⋊C4—46no—
704C22⋊C4—46no—
705C22⋊C4—46no—
706C42—212no—
707C42—212no—
708C42—26no—
709C42—26no—
710C42—212no—
711C42—212no—
712C42—43no—
713C42—43no—
714C42—46no—
715C42—412no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—26no—
721C23—26no—
722C23—26no—
723C23—26no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—26no—
728C23—26no—
729C23—26no—
730C23—26no—
731C23—26no—
732C23—26no—
733C23—26no—
734C23—412no—
735C23—412no—
736C23—412no—
737C23—86no—
738C23—86no—
739C23—86no—
740C23—86no—
741C23C22×#4112yes—
742C23C2×H(5,𝔽2)12yes—
743C23#58512yes—
744C23C2611yescharacteristic
745Q8—224no—
746Q8—86no—
747Q8#538116yescomplemented
748D4—424no—
749D4—424no—
750D4—424no—
751D4—424no—
752D4—86no—
753D4—812no—
754D4—812no—
755D4—1612no—
756D4—166no—
757D4—1612no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—23no—
761C2×C4—23no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—224no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—23no—
773C2×C4—26no—
774C2×C4—23no—
775C2×C4—26no—
776C2×C4—26no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—26no—
780C2×C4—26no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—23no—
789C2×C4—26no—
790C2×C4—23no—
791C2×C4—22no—
792C2×C4—23no—
793C2×C4—26no—
794C2×C4—23no—
795C2×C4—22no—
796C2×C4—26no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—26no—
800C2×C4—22no—
801C2×C4—44no—
802C2×C4—424no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—424no—
806C2×C4—424no—
807C2×C4—86no—
808C2×C4—86no—
809C2×C4—1612no—
810C2×C4C22×#4116yes—
811C2×C4C22×#4116yes—
812C2×C4C2×H(5,𝔽2)12yes—
813C2×C4C2×H(5,𝔽2)12yes—
814C2×C4C2×H(5,𝔽2)16yes—
815C2×C4C2×H(5,𝔽2)16yes—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—46no—
823C22—46no—
824C22—46no—
825C22—46no—
826C22—46no—
827C22—46no—
828C22—46no—
829C22—46no—
830C22—46no—
831C22—46no—
832C22—46no—
833C22—46no—
834C22—46no—
835C22—46no—
836C22—824no—
837C22#351714yes—
838C22C23×#4111yescharacteristic
839C22C22×H(5,𝔽2)11yescharacteristic
840C22C22×H(5,𝔽2)11yescharacteristic
841C22C22×H(5,𝔽2)11yescharacteristic
842C22C2×#58511yescharacteristic
843C22H(7,𝔽2)11yescharacteristic
844C222−1+611yescharacteristic
845C4—22no—
846C4—22no—
847C4—26no—
848C4—46no—
849C4—42no—
850C4—46no—
851C4—42no—
852C4—42no—
853C4—43no—
854C4—43no—
855C4—42no—
856C4—46no—
857C4—46no—
858C4—42no—
859C4—42no—
860C4C2×#538112yes—
861C2—24no—
862C2—86no—
863C2—86no—
864C2C22×#53811yescharacteristic
865C2C2×#351711yescharacteristic
866C2#6285111yescharacteristic
867C2#6289511yescharacteristic
868C2#6289711yescharacteristic
869C2#6289911yescharacteristic
870C2#6291611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42907C2semidirect
2. #42895C2semidirect
3. #42855C2semidirect
4. #42838C2semidirect
5. #39383C2semidirect
6. #39375C2semidirect
7. #39144C2semidirect
8. #37493C2semidirect
9. #36577C2semidirect
10. #36576C2semidirect
11. #36429C2semidirect
12. #36049C2semidirect
13. #36029C2semidirect
14. #36005C2semidirect
15. #35898C2semidirect
16. #35005C2semidirect
17. #34570C2semidirect
18. #34294C2semidirect
19. C2×#2341C2semidirect
21. C2×#557C22semidirect
24. C2×#550C22semidirect
27. C2×#520C22semidirect
33. #2829C22semidirect
34. #2828C22semidirect
35. #2780C22semidirect
36. #2779C22semidirect
37. #2778C22semidirect
38. #2733C22semidirect
39. #2727C22semidirect
40. #2714C22semidirect
41. #2710C22semidirect
42. #2708C22semidirect
43. #2682C22semidirect
44. #2682C22semidirect
45. #2661C22semidirect
46. #2653C22semidirect
47. #2652C22semidirect
48. #2649C22semidirect
49. #2648C22semidirect
50. #2648C22semidirect
52. #2644C22semidirect
54. #2641C22semidirect
57. #2624C22semidirect
59. #2619C22semidirect
62. #2582C22semidirect
63. #2568C22semidirect
64. #2562C22semidirect
65. #2559C22semidirect
66. #2557C22semidirect
67. #2548C22semidirect
68. #2548C22semidirect
69. #2541C22semidirect
70. #2538C22semidirect
71. #2535C22semidirect
72. #2513C22semidirect
73. #2512C22semidirect
74. #2512C22semidirect
75. #2501C22semidirect
76. #2497C22semidirect
77. #2496C22semidirect
78. #2494C22semidirect
79. #2491C22semidirect
80. #2491C22semidirect
81. #2490C22semidirect
82. #2490C22semidirect
83. #2487C22semidirect
84. #2453C22semidirect
85. #2445C22semidirect
86. #2445C22semidirect
91. #2428C22semidirect
92. #2428C22semidirect
93. #2426C22semidirect
95. #2422C22semidirect
96. #2422C22semidirect
99. #2416C22semidirect
100. #2416C22semidirect
104. #2401C22semidirect
105. #2398C22semidirect
106. #2395C22semidirect
107. #2392C22semidirect
108. #2367C22semidirect
110. #2360C22semidirect
111. #2351C22semidirect
112. Q8×C4⋊C4C22semidirect
113. Q8×C4⋊C4C22semidirect
114. Q8×C4⋊C4C22semidirect
122. #2341C22semidirect
123. #2341C22semidirect
125. #2326C22semidirect
127. #2323C22semidirect
136. #2276C22semidirect
747. Q8#538semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#429072
#428952
#428552
#428382
#393832
#393752
#391442
#374932
#365772
#365762
#364292
#360492
#360292
#360052
#358982
#350052
#345702
#342942
C2×#23412